Maximum Flow
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
![**Traffic Flow Optimization for Emergency Evacuations**
A city seeks to determine how many vehicles can navigate its streets during an emergency, specifically focusing on evacuation from a school to a park. The diagram below outlines the routes between these locations, detailing their capacity and direction.
**Diagram Explanation:**
- **Nodes:**
- **School**: Starting point for evacuation.
- **Oak Street**, **Elm Street**: Intermediate routes leading to further connections.
- **1st Street**, **2nd Street**: Subsequent paths leading towards the destination.
- **Park**: Final destination.
- **Arrows**: Indicate the direction of vehicle flow between nodes.
**Connections and Capacities:**
- **Path A**: School to Oak Street, with a capacity of 15 vehicles.
- **Path B**: School to Elm Street, with a capacity of 15 vehicles.
- **Path C**: Oak Street to 1st Street, with a capacity of 30 vehicles.
- **Path D**: Oak Street to 2nd Street, with a capacity of 10 vehicles.
- **Path E**: Elm Street to 2nd Street, with a capacity of 5 vehicles.
- **Path F**: 1st Street to Park, with a capacity of 5 vehicles.
- **Path G**: 2nd Street to Park, with a capacity of 30 vehicles.
**Table of Path Capacities:**
| Path | Capacity |
|------|----------|
| A | 15 |
| B | 15 |
| C | 30 |
| D | 10 |
| E | 5 |
| F | 5 |
| G | 30 |
**Calculation Task:**
Determine the maximum flow of vehicles from the school to the park and provide the rounded answer to the nearest whole number.
- **Maximum Flow**: [Enter your calculated answer here]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca4639e1-ad6a-4442-8c8c-fb1994ba5fd4%2F8593765d-d821-4ed6-93d1-8c03ff8cab6a%2Fr55k6m_processed.png&w=3840&q=75)
Transcribed Image Text:**Traffic Flow Optimization for Emergency Evacuations**
A city seeks to determine how many vehicles can navigate its streets during an emergency, specifically focusing on evacuation from a school to a park. The diagram below outlines the routes between these locations, detailing their capacity and direction.
**Diagram Explanation:**
- **Nodes:**
- **School**: Starting point for evacuation.
- **Oak Street**, **Elm Street**: Intermediate routes leading to further connections.
- **1st Street**, **2nd Street**: Subsequent paths leading towards the destination.
- **Park**: Final destination.
- **Arrows**: Indicate the direction of vehicle flow between nodes.
**Connections and Capacities:**
- **Path A**: School to Oak Street, with a capacity of 15 vehicles.
- **Path B**: School to Elm Street, with a capacity of 15 vehicles.
- **Path C**: Oak Street to 1st Street, with a capacity of 30 vehicles.
- **Path D**: Oak Street to 2nd Street, with a capacity of 10 vehicles.
- **Path E**: Elm Street to 2nd Street, with a capacity of 5 vehicles.
- **Path F**: 1st Street to Park, with a capacity of 5 vehicles.
- **Path G**: 2nd Street to Park, with a capacity of 30 vehicles.
**Table of Path Capacities:**
| Path | Capacity |
|------|----------|
| A | 15 |
| B | 15 |
| C | 30 |
| D | 10 |
| E | 5 |
| F | 5 |
| G | 30 |
**Calculation Task:**
Determine the maximum flow of vehicles from the school to the park and provide the rounded answer to the nearest whole number.
- **Maximum Flow**: [Enter your calculated answer here]
Expert Solution
Calculation of maximum flow
To find out the number of vehicles that can move from school to park can be calculated using the backward flow.
Possible routes to Park:
Route F
Route G
Total Capacity of F and G = 5 + 30 = 35
Now,
Maximum flow at Street 1 = Route C = 30 (greater than Route F)
So, maximum flow at street 1 = Capacity of Route F = 5
Maximum flow at Street 2 = Route D + Route E = 10 + 5 = 15 (less than route G)
So, maximum flow at street 2 = Capacity of Route D + Route E = 15
Total flow from Street 1 and 2 = 5 + 15 = 20
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